Since ACuriousMind has already answered some of the question before, I'll focus on how to compute or tabulated results.

https://groupprops.subwiki.org/wiki/Main_Page is available, but is a work in progress. Some of the groups, you might want are tabulated there.

SAGE has commands for calculating group cohomologies of reasonably small groups. Try small groups to test out how much computation power you can use. This works for point groups at least the ones I have tried running.

For crystallography groups see them tabulated in https://arxiv.org/abs/1612.00846

In groups that come in integer family like S_n, SU(n), SO(2n) you may see stabilization which makes the computation much easier. You need to have n big enough though.